A spinning device of an open-end rotor spinning machine is known from EP 1 283 288 A2. A thread is spun in an open-end spinning device and is delivered to a winding device. For the defined laying of the delivered thread on a bobbin, a single motor-driven thread traversing device is provided. After a thread breakage, the thread end that thereby arises is wound onto the bobbin. In order to use this thread end for the re-attachment with a new thread, it must be sought out on the bobbin. For this purpose, a swivel-mounted suction nozzle that is subject to negative pressure is provided. In the event of a thread breakage, the suction nozzle swivels from a lower position upwards to the bobbin circumference of the bobbin and subjects the bobbin surface to suction. The bobbin is set in a rotational movement, such that, after a certain period of time, the thread end is captured by the suction nozzle and extracted by suction. Subsequently, additional operations take place in order to be able to use the thread end for re-attachment. For this purpose, the thread end is transferred by the suction nozzle to other devices. This approach is time-consuming, since the suction nozzle must first be placed in motion, and the thread end that is found must be transferred by corresponding movements to the other operation devices. In addition, the structural complexity and the required installation space are considerable.